In this study, we demonstrate that by merely limiting the As flux, the growth behavior and structural quality of Au-catalyzed GaAs nanowires can be modulated in molecular beam epitaxy. With decreasing the As flux through lowering the V/III ratio, GaAs nanowire growth is found to be slow and defect-free wurtzite structured GaAs nanowires can be obtained regardless of catalyst sizes. While, in the As-enrich environment (such as at relatively high V/III ratio), thinner nanowires can grow longer with fewer planar defects. Based on our extensive morphological, structural and compositional investigations, it is found that GaAs nanowires grown under an As-limited condition can lead to a thermodynamically controlled growth process, while, when the nanowires grown under a relative high V/III ratio, a typical kinetically dominated process is observed. This study provides a new insight for controlling the structural quality of III-V nanowires by tuning the group-V flux.